A class of congruences on a posemigroup

V-completions of partially ordered algebraic systems have been studied by many authors, see Jaffard [7]. In particular, Burgess and McFadden [3] considered V-completions of posemigroups by means of ideal systems. In seemingly unrelated work, McFadden [10] characterized certain what we shall call ‘strongly isotone’ m-homomorphisms on posemi-groups; while Bigard [1], Dubreil-Jacotin [6] and McFadden [11] studied group homomorphisms on posemigroups. By determining certain coreflections [8], we prove that any surjective isotone homomorphism on a posemigroup can be factored into an injective strongly isotone homomorphism followed by a surjective strongly isotone m-homorphism. This result is used to bring the previous theories together and to generalise them.     

On partial ordering of chief factors in solvable groups

The isomorphism classes of chief factors in a finite solvable group are partially ordered by taking one class higher than the other if a member of the first class appears as a chief factor of the action of the group on a member of the second class. Together with this partial ordering the characteristics of the chief factors are considered. It is shown that the two conditions found by G. Pazderski are not only necessary but also sufficient for a partially ordered set and a function to be representable as the poset of isomorphism classes of chief factors in a finite solvable group with the chief factors having the prescribed characteristics. In addition, the construction yields that every finite distributive lattice is the lattice of normal subgroups of some finite solvable group.     

蕴涵偏序半群的同态

在蕴涵偏序半群中引入了三类同态,讨论了它们的关系和性质,并且给出了三个同态定理     

Ordered optimal solutions and parametric minimum cut problems

In this paper, we present an algebraic sufficient condition for the existence of a selection of optimal solutions in a parametric optimization problem that are totally ordered, but not necessarily monotone. Based on this result, we present necessary and sufficient conditions that ensure the existence of totally ordered selections of minimum cuts for some classes of parametric maximum flow problems. These classes subsume the class studied by Arai et al. [Discrete Appl. Math. 41 (1993) 69–74] as a special case.     

On Chains in <Emphasis Type="BoldItalic">H</Emphasis>-Closed Topological Pospaces

We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space (H-closed topological semilattice) under which L contains a maximal (minimal) element. We also give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that a linearly ordered H-closed topological semilattice is an H-closed topological pospace and show that in general, this is not true. We construct an example of an H-closed topological pospace with a non-H-closed maximal chain and give sufficient conditions under which a maximal chain of an H-closed topological pospace is an H-closed topological pospace.     

ON CONE D.C. OPTIMIZATION AND CONJUGATE DUALITY

This paper derives first order necessary and sufficient conditions for unconstrained cone d.c. programming problems where the underlined space is partially ordered with respect to a cone. These conditions are given in terms of directional derivatives and subdifferentials of the component functions. Moreover, conjugate duality for cone d.c. optimization is discussed and weak duality theorem is proved in a more general partially ordered linear topological vector space (generalizing the results in [11]).     

Prime Radicals of Lattice κ-Ordered Algebras

The Kopytov order for any algebra over a field is considered. Necessary and sufficient conditions for an algebra to be a linearly ordered algebra are presented. Some results concerning the properties of ideals of linearly ordered algebras are obtained. Some examples of algebras with the Kopytov order are described. The Kopytov order for these examples induces the order on other algebraic objects. The purpose of this paper is to investigate a generalization of the concept of prime radical to lattice-ordered algebras over partially ordered fields. Prime radicals of l-algebras over partially ordered and directed fields are described. Some results concerning the properties of the lower weakly solvable l-radical of l-algebras are obtained. Necessary and sufficient conditions for the l-prime radical of an l-algebra to be equal to the lower weakly solvable l-radical of the l-algebra are presented.     

Collection of Finite Lattices Generated by a Poset

It is proved that the collection of all finite lattices with the same partially ordered set of meet-irreducible elements can be ordered in a natural way so that the obtained poset is a lattice. Necessary and sufficient conditions under which this lattice is Boolean, distributive and modular are given.     

Multiplicative Automorphisms of Incidence Algebras

We present necessary and sufficient conditions for a multiplicative automorphism of an incidence algebra of a finite partially ordered set X to be an inner automorphism. These conditions are related to the structure of X as a directed graph.     

Existence and uniqueness of positive solutions for a nonlinear fourth-order boundary value problem

This work presents sufficient conditions for the existence and uniqueness of a positive solution for a nonlinear fourth-order differential equation under Lidstone boundary conditions. Our analysis relies on a fixed point theorem in partially ordered sets.     

Ohkawa's theorem: There is a set of Bousfield classes

We give a simple proof of Ohkawa's theorem, that there is a set of Bousfield classes. The proof leads us to consider the partially ordered set of Ohkawa classes, especially as it compares to the partially ordered set of Bousfield classes.

     

Categorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties

A syntactic apparatus is introduced for the study of the algebraic properties of classes of partially ordered algebraic systems (a.k.a. partially ordered functors (pofunctors)). A Birkhoff-style order HSP theorem and a Mal’cev-style order SLP theorem are proved for partially ordered varieties and partially ordered quasivarieties, respectively, of partially ordered algebraic systems based on this syntactic apparatus. Finally, the notion of a finitely algebraizable partially-ordered quasi-variety, in the spirit of Pałasińska and Pigozzi, is introduced and some of the properties of these quasi-povarieties are explored in the categorical framework.      

半序Menger PM-空间中广义弱压缩映射的最佳逼近点定理

本文利用三个控制函数给出了半序Menger PM-空间中满足特定条件的广义弱压缩映射的最佳逼近点定理,并给出了最佳逼近点唯一的充分条件.进一步地,还给出了主要结果的一些推论.     

Efficient and weak efficient points in vector optimization with generalized cone convexity

In this paper, we present necessary and sufficient conditions of efficiency and weak efficiency under generalized cone-convexity and cone-subconvexity. The results are stated in partially ordered real linear spaces from a separation theorem between convex cones which need not be solid.     

On l-prime radicals of lattice ordered algebras

The Kopytov order for any algebras over a field is considered. The purpose of this paper is to investigate a generalization of the concept of prime radical to lattice ordered algebras over partially ordered fields. Prime radicals of l-algebras over partially ordered and directed fields are described. Some results concerning properties of the lower weakly solvable l-radical of l-algebras are obtained. Necessary and sufficient conditions for the l-prime radical of an l-algebra to be equal to the lower weakly solvable l-radical of an l-algebra are presented.     

The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules

The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C ₀ of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved.     

A fixed point theorem for multifunctions and an application

The main result is a fixed point theorem for compositions of chain faithful multifunctions (Corollary 2.3). The theorem is then applied to get sufficient conditions for the fixed point property of the product of two partially ordered sets.Presented by R. P. Dilworth.     

Posets of subgroups in p-groups

It is shown that certain classes of finite p-groups are characterized by the ranked partially ordered set of conjugacy classes of their subgroups.     

Equivalent conditions for generalized contractions on (ordered) metric spaces

We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188-1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238-2242] do follow from an earlier result of O’Regan and Petru?el [D. O’Regan and A. Petru?el, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241-1252].